Sound volume and decibels

Martin McBride, 2020-07-05
Tags sound synthesis decibels
Categories computer music sound synthesis

One important aspect of a sound is how loud it is. This is particularly important in music. We aren't just concerned with the overall volume of the music (of course, you will want to listen to music at you preferred volume, which can vary a lot depending on whether you it is background music, or a live gig).

But when creating music we are also very conscious of the relative volumes of the different instruments. This of course is usually part of mixing the final piece.

What do we mean by volume? Well a sound wave transfers energy from the sound source to our ears. The amount of energy transferred per second is called the power delivered by the sound.

The more power in the sound, the louder it is, of course. But the amazing thing about our ears is that they can sense over an astonishing range of power. If you imagine the tiniest whisper we can just about hear, and the loudest sound you can listen too without damaging your ears, then if fact the loud sound is a million times more powerful than the whisper.

Sound volume and decibels

We measure sound power (ie volume) in decibels (dB). Here are some examples of different sounds, and their approximate dB values:

  • 0 dB is almost silence - there could still be sounds but too quiet to hear.
  • 10 dB is the quietest sound you might just be able to hear.
  • 50 dB is the hum of a fridge.
  • 60 dB is normal conversation.
  • 70 dB is a TV set on quite a loud setting.
  • 80 dB is something like an alarm clock, that you would not want to hear for a long time.
  • 85 dB is the loudest sound you should be exposed to for prolonged periods - louder than this can be dangerous for your hearing.
  • 110 dB would be a very loud rock concert.
  • 140 dB is the pain threshold, it would physically hurt your ears to listen (and damage them over time).
  • 150 dB would permanently damage your ears.

It is important to realise that decibels are a logarithmic measure of sound power. Every time the decibel value goes up by 10, the sound power is multiplied by 10.

For example, a normal conversational of sound is about 10 dB higher than the hum of a fridge, which means it has 10 times the sound power. An alarm clock is 30 dB louder than a fridge, that means it has 1000 times the power (ie 10 times 10 times 10, because each increase of 10 dB multiplies the power by 10).

The reason we use a logarithmic scale is because a difference of 10 dB between two sounds seems like the same amount. For example:

  • A loud TV is 10 dB higher than normal conversation.
  • An alarm clock is 10 dB higher than a loud TV.

We perceive the difference between the TV and conversation as being amount to the difference between and alarm clock and a loud TV. In fact, alarm clock is 100 times more powerful than normal conversation. So decibels express what we experience, while power expresses what is actually happening in reality.

Relative decibels

Decibels are actually a relative scale. We can choose to set 0 dB at any level we choose. For example, we might decide that we are going to base our measurements on the volume of one note of a piano played at normal volume. We define that sound as being 0 dB. On that scale:

  • A note played a bit louder, with twice the power would be 3 dB (on the logarithmic scale, 3 dB is a power factor of about 1.99).
  • A note played a bit louder still, with four times the power would be 6 dB (on the logarithmic scale, 6 dB is a power factor of about 3.95).
  • A power chord, played loudly with both hands, with ten times the power would be 10 dB.
  • A jazz band, with several instruments reaching a crescendo, with a hundred times the power would be 20 dB.

But what about quieter sounds? Well decibels are logarithmic, so if a dB value is negative, we divide the power by the factor, rather than multiplying it:

  • A note played a bit quieter, with half the the power would be -3 dB (on the logarithmic scale, -3 dB is a power factor of about 1/2).
  • A note played a even quieter, with a quarter of the the power would be -6 dB (on the logarithmic scale, -6 dB is a power factor of about 1/4).
  • A note played a really quietly, with a tenth of the the power would be -10 dB (on the logarithmic scale, -10 dB is a power factor of about 1/10).

Computer music

In computer music systems, unlike in the physical world, there is an absolute maximum upper limit to the sound power. Sound amplitude is represented as a number with a maximum range, and it is literally impossible to create a sound amplitude that is higher than that. Obviously, the sound created can be fed into an amplifier and played as loud as you like, but within the computer system it has a fixed maximum value.

Some systems define this maximum value as 0 dB. This means that when you set the volume of any instrument in the system, it must always be negative (or at the very most zero). You define the volume of a sound by haow much you are reducing that sound realtive to the loudest it could possibly be.

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